Victim Antiq Hennis, 16 months old, was being pushed in a stroller by his mother, Cherisse Miller, and father, Anthony Hennis, 21, across Livonia Avenue near Bristol Street around 7:15 p.m. when he was struck on the left side of his head, police said. He was pronounced dead at Brookdale Hospital, police said.

PJ Smith for The Wall Street Journal

Cherisse Miller, the mother of shooting victim Antiq Hennis.

“That is a tragedy for his parents and family, for the entire community and for this entire city. Every child in this city is precious, and every child deserves our protection. And when a child dies, we all suffer and we all grieve. Today, we are all grieving,” Mayor Michael Bloomberg said at a news conference Monday with NYPD Commissioner Ray Kelly.

Before the incident, Mr. Hennis went to visit Ms. Miller, who lives in the Marcus Garvey Village housing projects on Rockaway Avenue with her son, Mr. Kelly said.

“The purpose of the visit was to pick-up the child and to take the child to visit Hennis’ grandmother. He puts him in the stroller, and when they get to the intersection of Livonia Avenue and Bristol Street on the northwest corner, four shots are fired,” Kelly said. No one else was hit, he said.

Antiq’s great grandmother, Lenore Steele, 72, said the child was fond of shows like SpongeBob SquarePants and Dora the Explorer. She said he had just started to walk and had a healthy appetite.

“He could eat, he loved to eat, always eating,” she said. “Since he started to walk, oh my god he was so jolly.”

Investigators found four. 45-caliber shell casings on the corner, and one fired bullet was found at 360 Bristol St., Kelly said. “The stroller had four bullet holes in it. It appears to be two entrance and two exit holes,” Mr. Kelly said.

It is unclear who fired the bullets. There have been no arrests, officials said.

Mr. Kelly said the “investigative premise” is that Mr. Hennis was the target of the shooting. He said the father has an extensive arrest record that includes drug and weapons possession charges.

“Mr. Hennis has not been cooperative with us. He has not answered questions. We’re still trying to, obviously, determine his contacts. He has an extensive arrest record, so we are looking into his relationships with other people,” Mr. Kelly said.

At a press conference near the crime scene on Monday, community leader Tony Herbert said he and another community leader had been in contact with the alleged shooter and that they would deliver the suspect to police later in the day. He would not go into further details, saying he did not want to compromise the investigation.

The suspect was a described as a black male running from the scene, but as of Monday afternoon, investigators did not have many leads beyond that, Mr. Kelly said.

Mayor Bloomberg lashed out at the news conference at the flow of illegal guns to New York City and a federal judge’s recent ruling calling for a monitor to oversee stop-and-frisk.

“You can bet that the guns the perpetrators used were illegally possessed and originally purchased in a different state,” Mayor Bloomberg said, adding that is happens “over and over again.”

“It is nothing short of insanity, and it’s why we are going to continue to press lawmakers in Washington and lawmakers in every state with weak laws to wake up, show some courage and pass common-sense laws to protect the public,” he said.

Until that happens, Mayor Bloomberg said, the NYPD will continue using “pro-active policing tactics.”

“So the ideologues on the far right will continue to tell us our gun laws don’t need to be fixed. And the ideologues on the left will continue to tell us we need to handcuff the police officers who have been unfathomably successful in reducing violent crime,” Mayor Bloomberg said.

On Monday, a temporary memorial was set up outside the four-story apartment building where Antiq lived.

Family, friends and neighbors consoled the boy’s mother, who sat on the stoop outside.

“He’s just a happy little kid,” said Maxine Tasher, 40. “He just started his life.”

She called the violence in the neighborhood “unbearable.”

“All the politicians who come here don’t do anything for the neighborhood. I am going to be very careful [about] who I vote for this year,” Ms. Tasher said. ”If you come around here, it’s like a war zone. The violence needs to stop.”